{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#Snippets and Programs from Chapter 6: Drawing Geometric Shapes and Fractals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1065c8d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#P151: Drawing a Circle\n",
    "'''\n",
    "Example of using matplotlib's Circle patch\n",
    "'''\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def create_circle():\n",
    "    circle = plt.Circle((0, 0), radius = 0.5)\n",
    "    return circle\n",
    "def show_shape(patch):\n",
    "    ax = plt.gca()\n",
    "    ax.add_patch(patch)\n",
    "    plt.axis('scaled')\n",
    "    plt.show()\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    c = create_circle()\n",
    "    show_shape(c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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PPwK8uFXO1nTFXq03ar02yYVJTptLF28FWAtcNbK+Wt6nUQV8PskFSQ5f7sYMYE1Vbe4f\nbwbWtA5YrK9H72VbulFrlnN9E3AK8JZ+/QTgncBhS9S0oWz178kieHpVXZtkN2Bjkkv7K/OqU1U1\nl3uaBgmKqnruPA77HrBuZP2R/XNbtbmea5IPAFsSklur8fdpHffuCa54VXVt//OGJJ+mG26tpqDY\nnGT3qrouyR7A9a0DlnvoMX6j1sFJdkjyS8xwo9ZK0r8JUw6im8hd6S4A9k6yV5Id6Cagz1rmNi2a\nJDsleVD/eGfgQFbH+zbqLODQ/vGhwGdaBwzSo5hNkoOAvwUeTnej1jeq6nlVdUmSqRu17mR13Kj1\n9iRPouuufwc4Ypnbs2BVdWeS1wCfA7YDTquqby5zsxbTGuDTSaD7fHy8qs5b3ibNX5LTgWcCD+9v\nkDwWOAk4M8lhwCbgJc1yVv5nUdLQlnvoIWkFMCgkNRkUkpoMCklNBoWkJoNCUpNBIanJoJDU9P9j\noOKBcf70MAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106953390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#P153: A growing circle\n",
    "'''\n",
    "The animation is not viiewable in notebook. See:\n",
    "http://jakevdp.github.io/blog/2013/05/12/embedding-matplotlib-animations/\n",
    "\n",
    "\n",
    "A growing circle\n",
    "'''\n",
    "\n",
    "from matplotlib import pyplot as plt\n",
    "from matplotlib import animation\n",
    "\n",
    "def create_circle():\n",
    "    circle = plt.Circle((0, 0), 0.05)\n",
    "    return circle\n",
    "\n",
    "def update_radius(i, circle):\n",
    "    circle.radius = i*0.5\n",
    "    return circle,\n",
    "\n",
    "def create_animation():\n",
    "    fig = plt.gcf()\n",
    "    ax = plt.axes(xlim=(-10, 10), ylim=(-10, 10))\n",
    "    ax.set_aspect('equal')\n",
    "    circle = create_circle()\n",
    "    ax.add_patch(circle)\n",
    "    anim = animation.FuncAnimation(fig, update_radius, fargs = (circle,), frames=30, interval=50)\n",
    "    plt.title('Simple Circle Animation')\n",
    "    plt.show()\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    create_animation()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Enter the initial velocity (m/s): 25\n",
      "Enter the angle of projection (degrees): 60\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x106958320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#P156: Animating a projectile's projectory\n",
    "'''\n",
    "Animate the trajectory of an object in projectile motion\n",
    "'''\n",
    "from matplotlib import pyplot as plt\n",
    "from matplotlib import animation\n",
    "import math\n",
    "g = 9.8\n",
    "\n",
    "def get_intervals(u, theta):\n",
    "    t_flight = 2*u*math.sin(theta)/g\n",
    "    intervals = []\n",
    "    start = 0\n",
    "    interval = 0.005\n",
    "    while start < t_flight:\n",
    "        intervals.append(start)\n",
    "        start = start + interval\n",
    "    return intervals\n",
    "\n",
    "def update_position(i, circle, intervals, u, theta):\n",
    "    t = intervals[i]\n",
    "    x = u*math.cos(theta)*t\n",
    "    y = u*math.sin(theta)*t - 0.5*g*t*t\n",
    "    circle.center = x, y\n",
    "    return circle,\n",
    "\n",
    "def create_animation(u, theta):\n",
    "    intervals = get_intervals(u, theta)\n",
    "    xmin = 0\n",
    "    xmax = u*math.cos(theta)*intervals[-1]\n",
    "    ymin = 0\n",
    "    t_max = u*math.sin(theta)/g\n",
    "    ymax = u*math.sin(theta)*t_max - 0.5*g*t_max**2\n",
    "    fig = plt.gcf()\n",
    "    ax = plt.axes(xlim=(xmin, xmax), ylim=(ymin, ymax))\n",
    "    circle = plt.Circle((xmin, ymin), 1.0)\n",
    "    ax.add_patch(circle)\n",
    "    anim = animation.FuncAnimation(fig, update_position,\n",
    "                        fargs=(circle, intervals, u, theta),\n",
    "                        frames=len(intervals), interval=1,\n",
    "                        repeat=False)\n",
    "    plt.title('Projectile Motion')\n",
    "    plt.xlabel('X')\n",
    "    plt.ylabel('Y')\n",
    "    plt.show()\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    try:\n",
    "        u = float(input('Enter the initial velocity (m/s): '))\n",
    "        theta = float(input('Enter the angle of projection (degrees): '))\n",
    "    except ValueError:\n",
    "        print('You entered an invalid input')\n",
    "    else:\n",
    "        theta = math.radians(theta)\n",
    "        create_animation(u, theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Enter the number of iterations: 10000\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1065c88d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#P160: Random walk of a point in a plane\n",
    "'''\n",
    "Example of selecting a transformation from two equally probable\n",
    "transformations\n",
    "'''\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import random\n",
    "def transformation_1(p):\n",
    "    x = p[0]\n",
    "    y = p[1]\n",
    "    return x + 1, y - 1\n",
    "\n",
    "def transformation_2(p):\n",
    "    x = p[0]\n",
    "    y = p[1]\n",
    "    return x + 1, y + 1\n",
    "\n",
    "def transform(p):\n",
    "    # list of transformation functions\n",
    "    transformations = [transformation_1, transformation_2]\n",
    "    # pick a random transformation function and call it\n",
    "    t = random.choice(transformations)\n",
    "    x, y = t(p)\n",
    "    return x, y\n",
    "\n",
    "def build_trajectory(p, n):\n",
    "    x = [p[0]]\n",
    "    y = [p[1]]\n",
    "    for i in range(n):\n",
    "        p = transform(p)\n",
    "        x.append(p[0])\n",
    "        y.append(p[1])\n",
    "    return x, y\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    # initial point\n",
    "    p = (1, 1)\n",
    "    n = int(input('Enter the number of iterations: '))\n",
    "    x, y = build_trajectory(p, n)\n",
    "    # plot\n",
    "    plt.plot(x, y)\n",
    "    plt.xlabel('X')\n",
    "    plt.ylabel('Y')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Enter the number of points in the Fern: 10000\n"
     ]
    },
    {
     "data": {
      "image/png": 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JczLBAUUqNZfp018Gfky2Fm2JuBSVEG2kpGRzVt/H3NyBNDfnI605D1mK4dRw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OWIsi1GlPZadKVv05/6ZyTYYyeA1Pjf23waQV4QrRhrEMa7fGTSmQuBCoJtBGpIp1Uqv6m87PRw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\nVgk/eLMzwnCrNFMpf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      "text/plain": [
       "<matplotlib.figure.Figure at 0x106bf0898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#P165: Draw Barnsley Fern\n",
    "'''\n",
    "Draw Barnsley Fern\n",
    "'''\n",
    "import random\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def transformation_1(p):\n",
    "    x = p[0]\n",
    "    y = p[1]\n",
    "    x1 = 0.85*x + 0.04*y\n",
    "    y1 = -0.04*x + 0.85*y + 1.6\n",
    "    return x1, y1\n",
    "\n",
    "def transformation_2(p):\n",
    "    x = p[0]\n",
    "    y = p[1]\n",
    "    x1 = 0.2*x - 0.26*y\n",
    "    y1 = 0.23*x + 0.22*y + 1.6\n",
    "    return x1, y1\n",
    "\n",
    "def transformation_3(p):\n",
    "    x = p[0]\n",
    "    y = p[1]\n",
    "    x1 = -0.15*x + 0.28*y\n",
    "    y1 = 0.26*x  + 0.24*y + 0.44\n",
    "    return x1, y1\n",
    "\n",
    "def transformation_4(p):\n",
    "    x = p[0]\n",
    "    y = p[1]\n",
    "    x1 = 0\n",
    "    y1 = 0.16*y\n",
    "    return x1, y1\n",
    "\n",
    "def get_index(probability):\n",
    "    r = random.random()\n",
    "    c_probability = 0\n",
    "    sum_probability = []\n",
    "    for p in probability:\n",
    "        c_probability += p\n",
    "        sum_probability.append(c_probability)\n",
    "    for item, sp in enumerate(sum_probability):\n",
    "        if r <= sp:\n",
    "            return item\n",
    "    return len(probability)-1\n",
    "\n",
    "def transform(p):\n",
    "    # list of transformation functions\n",
    "    transformations = [transformation_1, transformation_2,\n",
    "                           transformation_3, transformation_4]\n",
    "    probability = [0.85, 0.07, 0.07, 0.01]\n",
    "    # pick a random transformation function and call it\n",
    "    tindex = get_index(probability)\n",
    "    t = transformations[tindex]\n",
    "    x, y = t(p)\n",
    "    return x, y\n",
    "\n",
    "def draw_fern(n):\n",
    "    # We start with (0, 0)\n",
    "    x = [0]\n",
    "    y = [0]\n",
    "    x1, y1 = 0, 0\n",
    "    for i in range(n):\n",
    "       x1, y1 = transform((x1, y1))\n",
    "       x.append(x1)\n",
    "       y.append(y1)\n",
    "    return x, y\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    n = int(input('Enter the number of points in the Fern: '))\n",
    "    x, y = draw_fern(n)\n",
    "    # Plot the points\n",
    "    plt.plot(x, y, 'o')\n",
    "    plt.title('Fern with {0} points'.format(n))\n",
    "    plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1067822e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#P174: Example of using the imshow() function\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.cm as cm\n",
    "import random\n",
    "\n",
    "def initialize_image(x_p, y_p): \n",
    "    image = []\n",
    "    for i in range(y_p):\n",
    "        x_colors = []\n",
    "        for j in range(x_p):\n",
    "            x_colors.append(0)\n",
    "        image.append(x_colors)\n",
    "    return image\n",
    "\n",
    "def color_points():\n",
    "    x_p = 20\n",
    "    y_p = 20\n",
    "    image = initialize_image(x_p, y_p)\n",
    "    for i in range(y_p):\n",
    "        for j in range(x_p):\n",
    "            image[i][j] = random.randint(0, 10)\n",
    "    plt.imshow(image, origin='lower', extent=(0, 5, 0, 5),\n",
    "               cmap=cm.Greys_r, interpolation='nearest')\n",
    "    plt.colorbar()\n",
    "    plt.show()\n",
    "    \n",
    "if __name__ == '__main__':\n",
    "    color_points()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.4.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
